Fluid Mechanics
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Study of fluids and the including forces is called as Fluid mechanics. Fluid Mechanics is divided into following parts.
Fluid statics which is the fluids study at rest,
Fluid dynamics which is the study of fluids in motion. It is sub branch of Continuum Mechanics
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Bernoulli's Equation in Fluid Mechanics
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Bernoulli's equation can be written in following way for steady and incompressible flow along a streamline,
P/p + V2/2 + gz = Constatnt
It can be easily seen that Bernoulli’s equation is form of conservation of energy if heat transfer and work is not done.
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| Bernoulli's Equation in terms of Head |
Bernoulli's equation can be written in terms of head as below
P/pg + V2/2g + z = Constatnt
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Navier Stokes equations
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The General form of the equation can be written as
The general form of the Navier–Stokes equations for the conservation of momentum is:
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Newton's law of cooling
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According to Newton’s law of cooling “ heat loss rate of a body is proportional to the difference in temperatures between the its surrounding and its body”. In differential equation that law can be written as :
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where
 : fluid density,
 : material derivative
 : velocity vector,
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 : body force vector
surface forces applied on a fluid particle can be written as
where
 : is a tensor that
 : are normal stresses,
: are tangential stresses (shear stresses).
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Dimensionless Parameters
Reynolds Number: Reynolds number is a dimensionless number which measure the ratio of forces due to inertia to the forces due to viscosity
Re = ?.V2L2/ µ.V.L
Prandtl Number: It is a dimensionless combination of three properties of a material 1) heat capacity 2) viscosity and 3) thermal conductivity:
Npr = Cp. µ /k
Nusselt number: It explains that how important conduction is compared to convection and It is defined as:
NNu = hD/k
Grashof number: It is a dimensionless parameter and used to model natural convection and defined as:
NGr L3?2ß?T/µ2
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